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Alkali metal‐doped boron clusters have captured much attention because of their novel electronic properties and structural evolution. In the study of RbBn0/− (n = 2–12) clusters, the minimum global search of the potential energy surface and structure optimization at the level of PBE1PBE by using the CALYPSO method and Gaussian package coupled with DFT calculation; the geometrical structures and electronic properties are systematically investigated. At n = 8, the ground‐state structures are composed of an Rb atom above B atoms, forming a structurally stable pagoda cone. By stability analysis and charge transfer calculation, the RbB8− cluster shows more stability. It found that s‐p hybridization between Rb atom and B atoms as well as s‐p hybridization between B atoms is one of the reasons for the outstanding stability exhibited in the RbB80/− clusters by using DOS and HOMO–LUMO orbital contour maps. The chemical bonding of the RbB80/− groups was analyzed by using the AdNDP method, and B atoms with larger numbers readily form multi‐center chemical bonds with the Rb atom. From the results of the bonding analysis, the interaction between the Rb atom and B atoms strengthens the stability of the RbB80/− clusters. It is hoped that this work provides a direction for experimental manipulation. [ABSTRACT FROM AUTHOR]

In this paper, we used CALYPSO program which is conjuncted with DFT to investigate Li doped small-sized neutral Bn clusters. From ground-state and low energy structures, the properties and geometric significance of Li-doped boron clusters are greatly affected. Except for LiB9, which adds a B atom on preceding LiB8 boron wheel, the ground-state clusters of LiBn are formed by replacing the terminal boron atom of the Bn+1 clusters in the same size with a Li atom or by adding a Li atom to the Bn clusters. The transition point from 2 to 3D configuration of LiBn clusters appears at n = 5. The stability of LiBn clusters was analyzed by calculating the average binding energy, Gibbs free energy, first-order differential energy, second-order differential energy, HOMO–LUMO gap (the energy gap between the highest occupied and lowest unoccupied molecular orbital) and charge transfer. The results show that the LiB11 cluster with excellent symmetry and planar structure is the relative most stable structure. Molecular orbital and chemical bonding analysis indicated that the main reason for the stability of the LiB11 cluster is mainly due to the strong s-p bonding of B–B. [ABSTRACT FROM AUTHOR]

In this paper, the geometric structure and physicochemical properties of Li2Bn0/− (n = 1–12) clusters were investigated using CALYPSO structure prediction software in combination with density functional theory at B3LYP/6-311G level. The results suggest that the doping of Li atoms has a significant effect on the ground state geometry of the Bn clusters. The stability changes with the increase in the number of boron atoms. Then two stable ground state structures, Li2B8 and Li2B9−, are selected for further analyzing their molecular orbitals and bonding properties. It is demonstrated that the stability of the Li2Bn0/− (n = 1–12) clusters originates from the s–p hybridization between B–B and Li–B. It is expected that this work can provide some references for future research on boron-based nanomaterials. [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Mg 2 Bn0/– (n = 1–12) clusters has be elucidated. • The corresponding ground state structures are determined. • The local stable ground state structure is found. • The properties of electrons and bonds of the most stable isomers are discussed. In this paper, a global search for the lowest energy structure of Mg 2 B n 0/- (n = 1–12) clusters is performed based on Density functional theory combined with the particle swarm optimization algorithm program CALYPSO. The geometry, stability, charge transfer, and bonding properties of the clusters were analyzed at the B3LYP/def2-tzvp level. Then Mg 2 B 8 with high symmetry D 4h was found to be the magic numbers cluster among them. The doped clusters Mg 2 B n 0/− were compared with the pure boron clusters B n+2 0/− (n = 1–12) at the same level. The following results are obtained: as the number of boron atoms increases, the boron clusters doped with Mg atoms change from a two-dimensional planar or quasi-plane structure to a three-dimensional structure. The doped magnesium atoms are always positively charged in the convex capped position. And the doping of Mg atoms drives the overall stabilization of the boron clusters and makes the clusters more compact. There is a large amount of charge transfer between the Mg atom and the B atom, and the main orbitals involved are the S and p orbitals. There are strong interactions between the two atoms of boron and magnesium. Through the analysis of the bonding properties, it was found that the s-p hybridization mode between Mg B is the main reason for the enhanced cluster stability. [Display omitted] [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Mg 2 Bn0/– (n = 1–12) clusters has be elucidated. • The corresponding ground state structures are determined. • The local stable ground state structure is found. • The properties of electrons and bonds of the most stable isomers are discussed. In this paper, a global search for the lowest energy structure of Mg 2 B n 0/- (n = 1–12) clusters is performed based on Density functional theory combined with the particle swarm optimization algorithm program CALYPSO. The geometry, stability, charge transfer, and bonding properties of the clusters were analyzed at the B3LYP/def2-tzvp level. Then Mg 2 B 8 with high symmetry D 4h was found to be the magic numbers cluster among them. The doped clusters Mg 2 B n 0/− were compared with the pure boron clusters B n+2 0/− (n = 1–12) at the same level. The following results are obtained: as the number of boron atoms increases, the boron clusters doped with Mg atoms change from a two-dimensional planar or quasi-plane structure to a three-dimensional structure. The doped magnesium atoms are always positively charged in the convex capped position. And the doping of Mg atoms drives the overall stabilization of the boron clusters and makes the clusters more compact. There is a large amount of charge transfer between the Mg atom and the B atom, and the main orbitals involved are the S and p orbitals. There are strong interactions between the two atoms of boron and magnesium. Through the analysis of the bonding properties, it was found that the s-p hybridization mode between Mg B is the main reason for the enhanced cluster stability. [Display omitted] [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Ca 2 Mg n – (n=1-15) clusters has be elucidated. • The corresponding ground state structures are determined. • One of the most stable structural units are found. • The properties of electrons and bonds of the most stable isomers are discussed. In recent years, the structure and properties of alkaline earth metal-doped Mg clusters have attracted much attention. Here, we investigated the structural properties, stability analysis, chemical bonding properties and charge transfer properties of Ca 2 Mg n ˉ (n=1-15) nanoclusters by using the efficient CALYPSO structure search software and the DFT full domain search method based on B3PW91 level calculation. It is found that most of their ground state structures can inherit pure Mg n+2 ˉ (n=1-15) clusters with high symmetry. We further compare the experimental and theoretical PES spectral data using pure Mg n+2 ˉ (n=1-15) and find a high agreement, which also indicating the validity of my calculated all-domain most stable structure. We found the outstanding stability of the pentagonal Ca 2 Mg 7 ˉ by stability analysis. Charge transfer occurred in all Ca 2 Mg n ˉ clusters, and this transfer was from Ca to Mg. The chemical bonding properties and molecular orbital revealed that the contribution of Mg- s and Mg- p to the molecular orbitals led to the formation of strong Mg-Mg bonds in the Ca 2 Mg 7 ˉ cluster, the s-p hybridization between Ca and Mg atoms and between Mg and Mg atoms also led to more powerful Mg-Mg bonds and Ca-Mg bonds, which is strong evidence for the stability of the Ca 2 Mg 7 ˉ clusters. [ABSTRACT FROM AUTHOR]

Projects about magnesium-based doped of transition metal have constantly attracted much attention in cluster science, while the research of Co, Fe, Ni doped Mid-Sized Mg16 clusters has not been reported. Here, the geometric construction and electronic properties of neutral and negative Mg16X (X = Co, Fe, Ni) clusters were researched by unbiased CALYPSO structure search codes and subsequent DFT calculations at the B3PW91 level. The results show that Fe and Co atoms are more likely to replace the central bits of the caged Mg170/− cluster, but the excellent and stable configuration of the Mg170/− cluster is perfectly maintained. Simultaneously, the doping of Co and Fe can cause the cluster to produce the corresponding magnetic moment. The caged Mg16Co− clusters with a central Co atom have good binding energy, local charge transfer and HOMO–LUMO gap according to stability analysis, which indicates that Mg16Co− clusters has better relative stability. In addition, it is found that there is an intense interaction between Mg-3s, p and Co-3d AO (molecular orbitals) through the analysis of molecular orbitals and adaptive natural density partitioning (AdNDP), which may be the main reason for the high stability of Mg16Co− clusters. [ABSTRACT FROM AUTHOR]

Bimetallic clusters have received extensive attention due to the changes in their properties and structures. Therefore, the structure and electronic configuration of medium-size Sr-doped magnesium clusters were studied in this work. The CALYPSO (crystal structure analysis by particle swarm optimization) algorithm and DFT (density functional theory) were applied to search, correct energy, and optimize geometry for stable low-energy structures. We described the structural evolution and characteristics of SrmMgn0/− (m = 1,2; n = 10–15) clusters, and found that a few ground-state isomers can maintain the same structure framework as the corresponding pure magnesium clusters. Through relative stability analysis, the SrMg13− cluster with a pyramid shape and Sr2Mg11 cluster with a pagoda-like shape were determined to be the most stable structures. Further analysis of the molecular orbitals and bonding characteristics of SrMg13− and Sr2Mg11 clusters also revealed a strong interaction between Sr and Mg atoms and the s–p bonding of Mg–Mg, which may be the main reason for the high stability of these clusters. We hope that this study will provide guidance for future doping of pure magnesium clusters. [ABSTRACT FROM AUTHOR]

In this work, the electronic structure, optical properties and thermoelectric properties of the GeI2 monolayer are calculated by the first principles with the Boltzmann transport equation. The monolayer is calculated as an indirect band gap semiconductor with an indirect band gap of a value 2.19 eV. This GeI2 monolayer is good for absorbing low-energy photons, and it is insensitive to high-energy photons. The material is stable at temperatures up to 600 K, so we calculated the thermal conductivity (KL), Seebeck coefficient (S), power factor (PF) and thermoelectric figure of merit (ZT) of the GeI2 monolayer at various carrier concentrations from 300 to 600 K. Due to the lower group velocity, the GeI2 monolayer has a lower thermal conductivity of 0.48 W/m K at 300K. In P-type doping, the power factor can up to 0.11 mW/m K2, and its ZT value is 4.04 at 600 K of the GeI2 monolayer, indicating that the GeI2 monolayer is a potential thermoelectric material. [ABSTRACT FROM AUTHOR]

To understand the effects of Cs on pure boron clusters, the growth mode, electronic properties, and bonding characteristics of CsB n 0/− (n = 2–12) clusters were discussed by CALYPSO combined with DFT method. Photoelectron spectra of the ground-state structures are reliable and efficient based on the accurate structure search method, which can provide theoretical information for future related studies. Through the study of the three valid criteria, we conclude that the CsB 8 and CsB 8 − with point group symmetry C 7V have outstanding stability and electronic properties. The orbital composition analysis indicates that the molecular orbitals of these two clusters are mainly composed of B-2 s and B-2 p atomic orbitals (AOs), and there is a strong interaction between these two AOs. Furthermore, we also found that the high stability of CsB 8 and CsB 8 − clusters mainly originates from the s - p bonding, σ and π bonds of B–B, especially the CsB 8 − cluster has (σ+π) double aromaticity. • The evolution of the structures for CsB n (n = 2-12) clusters has be elucidated. • The corresponding ground state structures are determined. • It is found that the most stable isomer is a double pyramid structure with double aromaticity. • The molecular orbitals and bonding characteristics of the most stable structure are discussed by various methods. [ABSTRACT FROM AUTHOR]

The structures properties of Cu n+1 and Cu n Se clusters have been investigated using an unbiased CALYPSO structure searching method. Firstly, an unbiased search relying on several structurally different initial clusters have been undertaken. Subsequently, geometry optimization by means of density functional theory is carried out to determine the relative stability of various candidates for low lying clusters obtained from the unconstrained search. The results shown that the ground state Cu 9 cluster is found to prefer a unique and previously unrecognized structure, with the total energies much lower than all structures proposed in the literature so far. The Cu 2 Se cluster is the most stable geometries for Cu n Se clusters. Additionally, the calculated HOMO-LUMO gaps ranges from 1.27 to 2.85 eV, which make Cu n Se clusters suitable candidates in photocatalyst materials. Lastly, the molecular orbital energy and density of states; the adaptive natural density partitioning; the electron localization function, localized orbital locator and Mayer Bond order are also studied for the ground state to develop a deeper understanding on the electronic properties. [ABSTRACT FROM AUTHOR]

In this study, the unbiased crystal structure analysis by particle swarm optimisation (CALYPSO) combined with the density functional theory (DFT) method were used to perform a structure search for neutral Cs2Bn (n = 1–12) clusters, as well as the corresponding global minimum of the potential energy surface were determined. The ground-state structures of the Cs2Bn (n = 1–12) clusters have four types of geometries: planar, arch bridge, double pyramid, and shield shape. Subsequently, the relative stability of the ground-state structures was systematically analysed based on three effective rules, which indicates that the C7V Cs2B8 with a double pyramid structure has unusual stability. The results of the molecular orbitals (MOs) and density of states analysis (DOS) show that the B-2s and 2p atomic orbitals of Cs2B8 are the main components of MOs. In addition, from the results of adaptive natural density partitioning (AdNDP) and localised orbital locator (LOL), it can be seen that the excellent stability of Cs2B8 originates from the delocalised large π bonds with aromaticity and the s–p bonding of B–B. Our results reveal the structural growth mode of Cs2Bn clusters and enrich the chemical bonding properties of boron-based clusters. [ABSTRACT FROM AUTHOR]

Divalent metal clusters, such as alkaline-earth metal clusters, have drawn extensive attention because of the appealing size-evoked nonmetal-to-metal transition and attractive characters related to the size, shape, and doping of clusters. Herein, the structural properties of small-size neutral and anionic Mgn+1 and BaMgn (n = 2–10) clusters are investigated thoroughly through a combination of the CALYPSO software package and DFT optimization. The final calculation results indicate that with the increase in Mg atom number, Ba atoms are inclined to substitute Mg atoms located at the skeleton convex cap. What is worth mentioning is that BaMg9 cluster which presents tower framework possesses excellent stability in specified size range on account of the detailed analysis of bond energy, second-order energy difference, and the charge transfer. In addition, the analysis of the bonding characteristics manifests that the strong s–p interaction between Ba and Mg atomic orbitals is conducive to the improvement in the stability of BaMg9. [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Ba n Mg m 0/– (n = 1,2; m = 10–15) clusters has be elucidated. • The corresponding ground state structures are determined. • Two local stable ground state structures are found. • The properties of electrons and bonds of the most stable isomers are discussed. Projects about alkaline-earth metals doped magnesium are hot issues constantly in cluster science, while research in terms of Mid-Sized Ba atoms doped magnesium cluster was unreported. We adopted the CALYPSO method coupled with DFT calculation to simplify the process of structure searching at the range of Ba n Mg m 0/– (n = 1,2; m = 10–15) cluster. We found the doped Ba atoms tend to occupy convex capped sites in each structure. Meanwhile, the six-atom triangular prism as a major structure constructed the great mass of isomers. Based on the result of the relative stability survey, we selected BaMg 13 – and Ba 2 Mg 13 – to conduct further investigations, according to a different numbers of doped Ba atoms. Analysis of the bonding character manifests that the Mg- p orbital takes up the highest proportion for both BaMg 13 – and Ba 2 Mg 13 – cluster at HOMO, LUMO position as well as the existence of strong covalent bonds between Mg-Mg atoms and Ba-Mg atoms. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • This study used sesquiterpenoids with 97 carbon skeletons for model construction. • The scheme based on the DFT method combined with triple correction can accurately calculate Δ c H of sesquiterpenoid HEDFs. • We developed the MLR equation with only 4 features for predicting Δ c H for sesquiterpenoid HEDFs. • The proposed DFT-QSPR scheme can effectively guide the design of novel sesquiterpenoid HDEFs. Sesquiterpenoids that are renewable and have high energy density and low freezing point are promising biomass high-energy–density fuels (HEDFs). The enthalpy of combustion (Δ c H) is the key characteristic to measure the heat energy content of HEDFs. Its accurate theoretical prediction and evaluation is essential for designing novel sesquiterpenoid HEDFs. Combining the screened and optimized density functional theory (DFT) method with triple computational correction, we presented a standardized calculation scheme for Δ c H with an average absolute error of only 2.6 % by 295 structurally diverse sesquiterpenoid HEDFs. Then, the extreme gradient boosting (XGBoost) algorithm was used to determine the correlation between the calculated Δ c H and 54 quantum chemical (QC) descriptors and the shapley additive explanation (SHAP) method to elucidate the key factors affecting Δ c H. Lastly, a quantitative structure–property relationship (QSPR) prediction model with only four QC features was constructed by using the SHAP results via the multiple linear regression (MLR) algorithms. Notably, the model has excellent prediction performance, decreased complexity, and improved applicability. The coefficient of determination (R 2) of the internal training set and external test set of the model are 0.957 and 0.956, while the root mean square error (RMSE) are 8.626 kcal/mol and 9.012 kcal/mol, respectively. The proposed DFT-QSPR (the ingenious combination of DFT and QSPR) scheme can effectively guide the design of Δ c H of novel sesquiterpenoid HDEFs. [ABSTRACT FROM AUTHOR]

The elastic anisotropy and thermodynamic properties of the recently synthesized Pnnm-CN have been investigated using first-principles calculations under high temperature and high pressure. The calculated equilibrium crystal parameters and normalized volume dependence of the resulting pressure agree with available experimental and theoretical results. With in the considered pressure range of 0-90GPa, the dependences of the bulk modulus, Young's modulus, and shear modulus on the crystal orientation for Pnnm-CN have been systematically studied. The results show that the Pnnm-CN exhibits a well-pronounced elastic anisotropy. The incompressibility is largest along the c-axis. For tension or compression loading, the Pnnm-CN is stiffest along [001] and the most obedient along [100] direction. On the basis of the quasi-harmonic Debye model, we have explored the Debye temperature, heat capacity, thermal expansion coefficient, and Gruneisen parameters within the pressure range of 0-90 GPa and temperature range of 0-1600K. [ABSTRACT FROM AUTHOR]

Using a newly developed particle swarm optimisation technique on crystal structural prediction, we have predicted an orthorhombicImm2 structure for TcN crystal, which is energetically much superior to the previously proposed NbO-type andR-3mstructures. The new phase is stable against decomposition into the mixture of Tc and N at ambient condition. The stability is confirmed by the subsequent calculations on the phonon dispersion curves and elastic constants. An analysis of the mechanical properties indicates thatImm2-TcN is incompressible and common hard material. The evidence of strong covalent bonding of Tc-N, which plays a leading role to form a hard material, is manifested by the partial densities of state analysis. In addition, the thermodynamic properties, such as Debye temperature, heat capacity, thermal expansion coefficient, and Grüneisen parameter of TcN are investigated by the quasi-harmonic Debye model. [ABSTRACT FROM PUBLISHER]

Here we reported the structures, electronic, spectral and thermodynamic properties of MB n −(M = La, Ce, Pr; n = 8, 9) clusters using Crystal structure Analysis by Particle Swarm Optimization (CALYPSO) searching method and density functional theory (DFT). Results found that the lowest structures of MB n −(M = La, Ce, Pr; n = 8, 9) possess the half-sandwich structure with C s symmetry, respectively. Based on the lowest energy structures, the electronic properties are analyzed by calculating charge transfer, electron localization function and polarizability; the photoelectron spectra, infrared spectra, Raman spectra and UV-vis spectra are computationally simulated to facilitate their spectral characterizations. At last, thermodynamic properties are symmetrically investigated for doped systems. We believe that our research will provide useful motivation for further experimental and theoretical investigations of lanthanide-doped boron based nanomaterials. [ABSTRACT FROM AUTHOR]

[Display omitted] • The evolution of the structures for Ba 2 Mg n (n = 1–10) clusters has be elucidated. • The corresponding ground state structures are determined. • A pagoda-like most-stable structure are found. • The properties of electrons and bonds of the most stable isomers are discussed. This paper reports systematic studies of small sized magnesium clusters doped with two barium atoms in both neutral and anionic species. The search, geometric optimization, and energy correction of stable and low-energy structures were completed using CALYPSO software package and DFT calculations. The structural evolution of Ba 2 Mg n 0/– clusters (n = 1–10) with increasing size were elucidated, and we found that most of the ground-state isomers of them inherit that of the corresponding pure Mg clusters well in terms of structure. After verifying the NBO (natural bond orbital) charge of the low-lying Ba 2 Mg n 0/– clusters (n = 1–10), a new fact was exposed: that all the doped Ba atoms in the structures are positively charged except in Ba 2 Mg–. A pagoda-like most-stable cluster Ba 2 Mg 8 with a HOMO-LUMO gap of 1.59 eV was found by relative stability analysis within the scope of our study. Further analyses of the molecular orbitals and bonding of Ba 2 Mg 8 clusters also revealed a strong interaction between Ba-6 s and Mg-3 p AOs, which may be the main reason for the high stability of Ba 2 Mg 8. We hope our studies will provide guidance for the synthesis and application of doped Mg-based nanomaterials in the future. [ABSTRACT FROM AUTHOR]

[Display omitted] • The evolution of the structures for Sr 2 Mg n (n =1–12) clusters has be elucidated. • The corresponding ground state structures are determined. • Several stable structural units are found. • The properties of electrons and bonds of the most stable isomers are discussed. Alkali earth metal clusters have been the subject of intense interest due to the wide range of applications and unique characteristics of transition from nonmetallic to metallic bond. In this work, the structural evolution and electronic properties of neutral and anionic strontium-doped magnesium clusters have been studied by structural search code of CALYPSO and subsequent calculation of DFT at B3PW91 level. The results reveled that most of the Sr 2 Mg n 0/– clusters are viewed as the substituted structures of corresponding pure magnesium clusters, in which the Sr atoms prefer to occupy the convex capped sites. Analysis of the natural population show that the Sr atoms always play the role of electron donor in the charge transfer process except for Sr 2 Mg 1-3 –. In the range of studied size, the neutral Sr 2 Mg 8 cluster with a tower-like structure and outstanding stability is uncovered. The molecular orbital and chemical bonding analysis indicate that the stronger Sr-Mg interaction lead to s-p hybridization between Sr and Mg atoms can stabilize the Sr 2 Mg 8 cluster. [ABSTRACT FROM AUTHOR]